Problem!!!

So yesterday I went to the social security office and finally changed my name after getting married. Only a year and 4 months late but that's OK. I know it's a long process to change everything (debit cards, utility bills, credit cards, car insurance paperwork... the list goes on.) I'm not going to lie, I waited this long because I didn't want to change everything, I've had the same name for 24 years so it was a tough decision on what name I was going to use. 

I went in thinking I'd leave Shannon Heit Ruddy but the lady informed me that I could not do that?? Not sure why, but my only options were, "Shannon Ashley Ruddy" or "Shannon Ashley Heit Ruddy." My dad is the last "Heit" and I knew the name was not going to go on anymore and I wanted to keep that name in the family in honor of my paternal grandparents. I didn't think twice when I had to loose the Heit or keep it and have 4 names until I got home and my aunt asked me legally what my middle and last name is? 

So my question to you, do I have 2 middle names or 2 last names? I've been googing this and can't find an answer. If I still don't know by the time the card comes in hopefully the DMV will know when I get a new license?